Solution
= Solution
The condition $A+A^*=0$ forces the diagonal entry $a$ to be purely imaginary and $c=-\overline b$. Thus every $A\in V$ has a unique expression
$$
A=
\begin{pmatrix}
ix&y+iz\\
-y+iz&-ix
\end{pmatrix},
\qquad x,y,z\in\mathbb R.
$$
The map $A\mapsto(x,y,z)$ is a real-linear isomorphism, so
$$
\boxed{V\cong\mathbb R^3.}
$$